DIPSY: A new Disc Instability Population SYnthesis, I. Modeling, evolution of individual systems, and tests

TL;DR

DIPSY addresses how companions form via disc instability by coupling star–disc formation with disc self-gravity, fragmentation, clump evolution, and multi-body dynamics in a computationally efficient 1D framework. It solves the diffusion equation for Σ with a variable α and tracks clump accretion, irradiation, mass loss, and N-body interactions, using torque densities and a dynamical-friction–based damping scheme to handle migration and eccentricity evolution. The model enables population synthesis across planetary to low-mass stellar regimes and demonstrates a wide range of possible system architectures, from non-fragmenting discs to multi-fragment systems with collisions and ejections. It highlights how interconnected processes—gas accretion, orbital migration, and N-body interactions—air significant influence on the inferred populations and emphasizes that model assumptions dramatically shape the outcomes. The work lays a foundation for quantitative comparisons with observations and identifies key limitations and avenues for future improvements, such as incorporating solids physics and refined torque treatments in self-gravitating discs.

Abstract

Disc instability (DI) is a model aimed at explaining the formation of companions through the fragmentation of the circumstellar gas disc. Furthermore, DI could explain the formation of part of the observed exoplanetary population. We aim to provide a new comprehensive global model for the formation of companions via DI. The latter leads for the companions to orbital migration and damping of the eccentricities and inclinations. As it evolves, the disc is continuously monitored for self-gravity and fragmentation. When the conditions are satisfied, one (or several) clumps are inserted. The evolution of the clumps is then followed in detail. We showcased the model by performing a number of simulations for various initial conditions, from simple non-fragmenting systems to complex systems with many fragments. We confirm that the DIPSY model is a comprehensive and versatile global model of companion formation via DI. It enables studies of the formation of companions with planetary to low stellar masses around primaries with final masses that range from the brown dwarf to the B-star regime. We conclude that it is necessary to consider the many interconnected processes such as gas accretion, orbital migration, and N-body interactions, as they strongly influence the inferred population of forming objects. It is also clear that model assumptions play a key role in the determination of the systems undergoing formation.

Figures (10)

• Figure 1: Schematic representation of the star and disc system, including its physical processes.
• Figure 2: Schematic overview of the physical processes related to fragmentation and the evolution of companions that are included in the global model.
• Figure 3: Evolution tracks of isolated clumps. Top left: Clump radius. Top right: Central density. Bottom left: Central temperature. Bottom right: Pre-collapse time for all clump masses. These tracks were first published in 2019MNRAS.488.4873H.
• Figure 4: Evolution of a system that becomes self-gravitating but that does not fragment. Left panel: Stellar mass, disc mass and disc size as a function of time. Right panel: Minimum $Q_\mathrm{Toomre}$ and $\alpha$ as a function of time. The black vertical line shows the end of infall. It should be noted that there two distinct y-axes in both panels to which the different quantities belong to.
• Figure 5: Evolution of a system forming a single (transient) fragment which is eventually accreted into the host star because of orbital migration. Top left: Stellar mass, disc mass and disc radius. Top right: Minimum $Q_\mathrm{Toomre}$ and $\alpha$. The stellar accretion rate is shown in black (see text Sect. \ref{['sec:sfrag']}). Middle left: Time evolution of fragment orbital separation $r_{\rm c}$ and mass $M_{\rm c}$. Middle right: Same with a zoom-in on the early phase, two variant calculations are shown additionally in black (see text Sect \ref{['sec:sfrag']}). Bottom left: Surface density, centred on the fragment (and thus at different absolute orbital distances), for a selection of times. Bottom right: Time evolution of the fragment radius, central and effective temperature as well as the disc temperature at the fragment's location.